Chapter 1120 The Peak of Human Mind!

In fact, regarding whether he is still a human being, Lu Zhou may not be able to answer this question now.

Although judging from the data on the physical examination sheet, the strengthening of the system does not seem to be reflected in the transformation of his DNA, but with his current thinking ability, it is obviously beyond the reach of ordinary humans—even beyond the scope of understanding.

If he remembered correctly, Professor Deligne had invited him to join the research on the standard conjecture when he first entered Princeton, that is, about six years ago.

Six years have now passed.

Obviously, no significant progress has been made on this topic until now.

Now, however, solving it is as easy as breathing.

Although a large part of the reason for this is that the grand unified theory provides a theoretical basis for proving this proposition, but even setting aside those conclusions that can be directly drawn through the grand unified theory, in just half an hour Solving so many problems is also quite a scary thing.

Even in his own eyes.

Taking a deep breath of the cold air to cool down the agitation in his chest, Lu Zhou looked at the line "Lefschetz standard conjecture, established!" on the whiteboard and was silent for a long time before speaking slowly.

"As we all know, the standard conjecture can be divided into two parts. The first half is Professor Grothendieck's extension of the Hard-Lefschetz theorem when studying Weil's conjecture, which is also known as the Lefschetz standard conjecture."

"The second half is Hodge's standard conjecture."

It seemed that he was entangled in some troublesome matter, and Lu Zhou frowned and thought for a long time.

The audience was silent.

Everyone is waiting for him to continue.

Under the gaze of countless expectant eyes, the frown suddenly relaxed, and Lu Zhou continued in a relaxed tone.

"never mind."

"Although it is only to demonstrate the application of the grand unified theory in the study of algebraic geometry problems..."

"But since it's all written here."

"Let's settle it together."

He didn't look at the shocked faces behind him, nor did he listen to the exclamations and unbelievable discussions that resounded through the venue.

Lu Zhou, who casually dropped this sentence, walked to the blank whiteboard next to him with complex emotions such as awe, emotion, and peace, and stopped for a while.

The standard conjecture is one of the most profound propositions in algebraic geometry.

Its profundity lies not only in its complex beauty, but also in its profound inferences.

Most directly, if the standard conjecture holds true, the Weil conjecture can be directly deduced through it, and it can be deduced that the effect of Frobenius on the cohomology group of smooth projective algebraic varieties is semi-simple, and even the algebraic closed chain in algebraic varieties can be deduced ( Algebraic cycle) numerical equivalence (numerical equivalence) and homology equivalence (homological equivalence) are the same equivalence relation and so on.

These are all known.

And there are theories that have yet to be explored.

It is no exaggeration to say that it is this conjecture that guides the development of modern algebraic geometry.

However, so far, its historical mission should be over.

As his hand lifted, the pen that had landed on the whiteboard moved.

[...When i≤n/2, the quadratic form x→(1)^i·L^(r2i)x.x on A^i(X)∩ker(L^(n2i+1)) is positive definite ...]

Among them, X is a smooth projective algebraic variety on the field k, l is a prime number that is relatively prime to the characteristics of k, H^i(X, Ql) is the i-order l-adic cohomology group of X, and the hyperplane of X and projective space Intersection is a subalgebraic variety of X.

This conjecture is known when X is an algebraic surface or a complex algebraic variety.

And now what he wants to prove is that under normal circumstances, it is also true!

Time passed by every minute and every second.

There are more and more calculations on the whiteboard.

Many people sitting in the audience, the speed of ingesting information, even gradually began to be unable to keep up with the speed of his writing on the blackboard.

Perelman, who was sitting under the stage with his arms folded and frowning, suddenly sat up straight, and his pupils staring directly at the whiteboard shrank into a single point in an instant.

Schultz, who was sitting not far from him, had almost the same reaction, and even let out an unbelievable exclamation.

"...Use the L^2 cohomology method to obtain the topological information of the compact quotient of complete manifolds, and extend the Hodge theory on compact manifolds to complete non-compact manifolds!"

"God... he, he is a genius!"

This is a property of the L^2 cohomology theory mentioned by Sir Attia in his paper on the study of discrete groups and elliptic operators published in the "Annual Mathematics" in 1976.

What is surprising is not only the ingeniousness of his conception, but what really astounds Schultz is that his use of these mathematical tools is as easy as breathing.

It was as if those mathematical tools were born for him.

Glancing at the stunned Schultz, Perelman, who hadn't spoken all this time, muttered a rare word.

"...This kind of obvious thing, even if you don't say it, everyone knows it."

Not far away.

Two old men sat there, staring at the whiteboard motionless.

At the moment when Lu Zhou successfully extended Hodge's theory on compact manifolds to complete non-compact manifolds, Professor Deligne suddenly broke the tacit understanding of silence and said.

"What do you think?"

Sitting next to him, Faltins did not speak.

After about half a minute, he shook his head.

"I might need a little time... maybe, I'm really old."

Deligne remained silent, looked at the stage with a complicated expression, and stopped speaking.

After so many years of friendship, it was the first time he heard that this guy admitted that he was old.

Although this is an indisputable fact, hearing this guy admit it with his own mouth still made him a little sad...

The same conversation is happening on the other side of the venue.

It's just that Mr. Qiu Chengtong was the one who asked the question, and Professor Tao was the one who answered it.

As an all-rounder in the field of mathematics, he was probably the only person in the venue who could keep up with writing on the whiteboard, except for Lu Zhou himself.

It's not easy though.

Even for him, it is quite a challenge to keep up with this rhythm.

"His thinking speed is too fast... To make an inappropriate analogy, the average person may ride a rocket... Maybe I ride a Space-X Falcon, but the essence is still a rocket, and there is no essential difference from other rockets. But he is different, he has already sat on something similar to a warp speed engine. When I was still walking down a line of thought step by step, he had already folded the whole paper in half, from the proposition The stem of the question jumps directly to the result part."

Because his wife works at NASA, he usually has a lot of contact with aerospace matters. Although he may not be professional, he still knows the model of the rocket.

Regarding this strange metaphor, Mr. Qiu didn't say anything, but silently moved his gaze to the almost filled whiteboard.

After a while, he clenched his fists and sighed softly.

"Nice job!"

...

There is no doubt that this is the most glorious moment in the history of Huaguo mathematics.

No, to be precise, it's not just the Huaguo mathematics community.

Even if you look at the world and look back at history, you may not be able to find a more glorious moment.

At this moment, what he ascended was not only the god's seat in the Temple of Mathematics, but also the pinnacle of human mind.

Standing in front of this whiteboard that connects the universe, no matter the nationality, race, or cultural background, it seems to have become pale and meaningless.

Standing at the height of species and civilization, all of this is too small.

With the last punctuation drop.

Everything is quiet.

In fact, as early as ten lines ago, there was no suspense in the result, but very few people could see it.

Withdrawing the pen that fell on the whiteboard, Lu Zhou took two steps back and looked at his results, as if looking at a work of art, for a long, long time.

About ten minutes passed before he turned around, faced the silent venue, and spoke slowly.

"The above is the proof of the standard conjecture."

The sound echoed in the empty arena.

There was a complete silence in the audience.

No one spoke.

There was no applause either.

The sluggish or dignified expressions of the audience in the front row have already told their mood and state at this moment. Everyone has not recovered from the double shock both visually and spiritually, so naturally they can't talk about their feelings.

Without pausing for too long, Lu Zhou glanced around the silent venue, and continued in an unhurried tone.

"In fact, the grand unified theory is the theme of this report."

"The proof of the standard conjecture is just an introduction. I hope that through my presentation, it will bring some inspiration for your future exploration of beautiful things."

"Just like what we have witnessed together at this moment, our theory has once again verified that our universe is perfect, and it conforms to the beauty of mathematics."

"Anyone else, do you have any questions?"

The silence in the audience continued.

Still no one spoke.

Shoulders loosen.

It felt like he had let go of a heavy burden, and Lu Zhou, who had been expressionless, suddenly had a pleasant smile on his face.

That smile is like the spring wind in early March. Although there is no special tension, it blows into the hearts of every listener.

"Since there is no one, then this report will end here."

"I will be here for these three days. If you have any new questions later, you can come to me here."

"Thanks."

The applause sounded like pouring rain.

Almost knocked off the ceiling of the stadium.

Lu Zhou couldn't see clearly in places that were too far away, but as far as he could see, the faces, young or old, were full of shock and madness without exception.

The whole world seemed to be re-wound, from the silent silence, it began to tick again.

The staff standing on both sides of the lecture hall, as well as the security personnel, all cast surprised glances into the venue, not quite understanding what happened.

Of course they won't understand.

Just like the beauty of mathematics, it will not open up to everyone.

However, for those who can understand it, this kind of beauty shocks the heart and reaches the depths of the soul.

Although there is no sound, it is like a song.

Bathed in the applause that resounded through the venue, Lu Zhou gently placed the marker pen in his hand that was destined to become a historical relic on the podium, took half a step back and bowed slightly, turned and walked to the audience.

The era of the standard conjecture is over.

Use this moment as a watershed moment.

Every minute in the future belongs to the new world!